Little is available in mathematics education research about what the teacher can anticipate from the students when applying inquiry-based learning (IBL). Even less is known about how to recognize and exploit on the spot when a mathematical domain, other than the one in focus, is activated in the students' minds. Yet, in tests, in everyday life, and the labour market, it is common to face problems that require interrelated mathematical thinking. Although one of the unique advantages of complex mathematics education (CME) is the coherence between different domains and CME has been practiced for over half a century in Hungary, the Hungarian line of IBL has only recently joined the international methodological mainstream. In this paper, I summarize a segment of IBL correspondent to CME and integrated mathematics education, and I illustrate the possible divergence of solutions during implementation with an example that emerged about a probability game in a fifth-grade class.